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+ | ===== Babylonian Astronomy ===== | ||
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+ | ==== Introduction ==== | ||
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+ | Within the Babylonian tradition of astronomy there have been two genres of texts: There are mathematical astronomy texts, which mostly consist of tables recording or calculating various statistics about the behavior of heavenly bodies. These texts themselves do not deal with the interpretation or prognostication of the events they record. The second type of document is the ' | ||
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+ | List of topics: | ||
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+ | - Basic terms and concepts | ||
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+ | - Mathematical Astronomy | ||
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+ | * [[Lunar Ephemerides]] | ||
+ | * [[Plantary Ephemerides]] | ||
+ | * [[Applications to Chronology]] | ||
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+ | - Non-mathematical Astronomy | ||
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+ | ==== Basic terms and concepts ==== | ||
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==== Metrological Units ==== | ==== Metrological Units ==== | ||
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Years were denoted by whole numbers starting from... | Years were denoted by whole numbers starting from... | ||
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- | == Lunal ephemerides == | ||
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- | The most commonly recorded observations of the Seleucid Period were the appearances of the new moon and full moon (during which we say the moon and sun are in conjunction and opposition, respectively). These sightings determined the lengths of the months. In addition, several other statistics were measured such as the velocity, longitude, and latitude of the moon at time of syzygy, and the length of daylight on that day. Such data was used to predict solar and lunar eclipses whose occurrence held deep significance in ancient Mesopotamian cultures. | ||
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- | At some point the Babylonians realized that the velocity of the sun along the ecliptic was not constant, but rather varied depending on its position. This perhaps was noticed due to the inequality in transition times between the two equinoxes (see Neugebauer pg. 56). The reason for this variation is that the earth' | ||
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- | To account for this variability the Babylonians used two schemes, evident implicitly in the calculated figures of the ephemerides tables and explicitly in the small number of procedure texts. Neugebauer names these schemes System A and System B. | ||
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- | == System A == | ||
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- | In this scheme the sun is presumed to move at one of two constant speeds on different arcs of the ecliptic. From 13 degrees Virgo to 27 degrees Pisces the sun is presumed to move one whole zodiac sign (30 degrees) in a month. For the rest of the year it moves slightly slower, namely 28;7,30 degrees per month. | ||
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- | == Layout of a tablet == | ||
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- | By way of illustration, | ||
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- | {{: | ||
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- | == Column 0 (T) == | ||
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- | The first column on the left side of the obverse gives the year and the months within, each one of which records a syzygy. Neugebauer calls this Column T. Here the records begin with year 146 of the Seleucid period, which began in 311 BC. Thus the year is 166 BC. The first month is Nisan, or April. Note the addition of an intercalary month at the end of 164 BC, in Rev. 19. | ||
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- | == Column I == | ||
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- | == Column II (B) == | ||
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- | This column records the longitude of the moon at the time of the new moon, measured relative to the ecliptic. These values are calculated sequentially based on the measurement of an initial value. The numbers on the left hand side are the degrees within the zodiac sign on the right. | ||
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- | Neugebauer has drawn up the table so that the two periods of the year with different velocities of the sun are separated by dashed lines. At a new moon the longitude of the moon at syzygy equals the longitude of the sun when it sets on the horizon. Thus the values of column III, which record the progress of the moon through the zodiac, also measure the movement of the sun. For example in obv. 6-12 the difference in successive entries is one whole zodiac sign, i.e. 30 degrees. In the next interval obv. 13-18 the differences of successive entries is 28;7,30 degrees. The change between the two months at the boundaries is an interpolated value between the two velocities. | ||
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- | == Column III (C) == | ||
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- | This column provides the length of daylight on the day of the given observation. In Neugebauer' | ||
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- | The entries for this column were calculated based on a trigonometric formula dependent on the latitude of the observer and the part of the ecliptic that the sun is in at that time, i.e. the time of the year. Rather than measuring their latitude directly, however, the Babylonians, | ||
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- | For the increments in daylight based on the sun's position λ along the ecliptic, calculations were made starting from 10 degrees into the sign of Aries (or hun is Sumerian) whose beginning point marks the vernal equinox where the daylight equals 12 hours, and from then on in increments of 30 degrees. | ||
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- | ^ λ ^ Length of daylight (in hours)^ | ||
- | | Aries/hun 10° | 12;00 | | ||
- | | Taurus/mul 10° | 13;20 | | ||
- | | Gemini/masz 10° | 14;08| | ||
- | | Cancer/ | ||
- | | Leo/ura 10° | 14;08 | | ||
- | | Virgo/apsin | 13;20 | | ||
- | | Libra/rin2 | 12;00 | | ||
- | | Scorpius/ | ||
- | | Sagittarius/ | ||
- | | Capricorn/ | ||
- | | Aquarius/ | ||
- | | Pisces/ | ||
- | (table from Neugebauer 1975, pg. 370) | ||
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- | Within these increments linear interpolation was used. Thus is the example text, the value in obv. 13 II is between hun 10° and mul 10°. The daylight increment over this interval of 30° is 1;20 hours, or 20°. Hence the daylight increment of 6;48,45° past hun 10° is 2/3 x 6;48,45° = 4;32,30, which is what is indicated in row 13, column III. | ||
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- | == Column IV (E) == | ||
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- | This column gives the latitude of the moon (more specifically its center) relative to the ecliptic, at the time of observation. It is measured in barleycorns (sze). For example, in obv. 1, the value is 3,12;8,39, or (3x60+12+8/ | ||
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- | The latitude of a given syzygy can easily be determined from the latitude of the previous syzygy and the rates by which the moon's latitude changes across the average syzygy period. In system A the moon's change in latitude is taken to be proportional to the sun's velocity (minus a correction factor for nodal precession), | ||
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- | In the example text, plus and minus signs in front of the latitudes - again inserted by Neugebauer - indicate which side of the ecliptic, above or below, the moon is at syzygy. | ||
- | A given entry in the column can be computed from the preceding syzygy' | ||
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- | == Column ??? (Ψ) == | ||
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- | This column measures the magnitude of the eclipse at the time of the recorded syzygy (full or new moon). | ||
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- | ???? | ||
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- | == Column V (F) == | ||
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- | This gives the velocity of the moon around the time of measurement (longitude? | ||
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- | == Column VI (G) == | ||
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- | This column gives a first approximation to the length of the lunar month in which the observation was made. It assumes a constant velocity of the sun (that of the faster arc), and is measured in terms of the deficiency from the average length (29 days), marked by the LAL sign. Neubegauer expresses the units in fractional large hours. E.g. in obv. 2 the length of the month Nisan was 29 days minus 0;57,03,45 large hours, or approximately 3 hours, 48 minutes, and 14 seconds. | ||
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- | == Column VII (J) == | ||
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- | This column consists lists a correction factor for the different velocity of the sun along the slower arc of the ecliptic. Because the discontinuity around the jump points in the arc, interpolated values are calculated for the transitional rows. | ||
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- | == Column VIII (K) == | ||